Local Reynolds number and thresholds of transition in shear flows

• Published in: Science China. Physics, mechanics & astronomy mechanics & astronomy, 2013-02, Vol.56 (2), p.263-269
• Main Authors: Tao, JianJun, Chen, ShiYi, Su, WeiDong
• Format: Article
• Language: English
• Subjects: Astronomy; Base flow; Classical and Continuum Physics; Couette flow; Couette流; Energy dissipation; Energy equation; Fluid dynamics; Fluid flow; Laminar flow; Observations and Techniques; Physics; Physics and Astronomy; Poiseuille流; Reynolds number; Shear flow; Thresholds; Turbulence; Turbulent flow; 剪切流动; 数值研究; 流体元件; 能量方程; 阈值; 雷诺数
• ISSN: 1674-7348; 1869-1927
• DOI: 10.1007/s11433-012-4955-7

Recent experimental and numerical investigations reveal that the onset of turbulence in plane-Poiseuille flow and plane- Couette flow has some similar stages separated with different threshold Reynolds numbers. Based on these observations and the energy equation of a disturbed fluid element, a local Reynolds number ReL is derived to represent the maximum ratio of the energy supplement to the energy dissipation in a cross section. It is shown that along the sequence of transition stages, which include transient localized turbulence, ＂equilibrium＂ localized turbulence, spatially intermittent but temporally persistent tur- bulence and uniform turbulence, the corresponding thresholds of ReL for plane-Couette flow, Hagen-Poiseuille flow and plane-Poiseuille flow are consistent, indicating that the critical （threshold） states during the laminar-turbulent transition are determined by the local properties of the base flow and are independent of global features, such as flow geometries （pipe or channel） and types of driving forces （shear driving or pressure driving）.